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Position dependent and stochastic thinning of point processes

A short probabilistic proof of Kallenberg's theorem [2] on thinning of point processes is given. It is extended to the case where the probability of deletion of a point depends on the position of the point and is itself random. The proof also leads easily to a statement about the rate of convergence in Renyi's theorem on thinning a renewal process.
Year of publication:
1979
Authors: Brown, Tim
Published in:
Stochastic Processes and their Applications. - Elsevier, ISSN 0304-4149. - Vol. 9.1979, 2, p. 189-193
Publisher: Elsevier
Keywords: Point process random measure thinning convergence in distribution Poisson process Cox process
Type of publication: Article
Source:
Persistent link: https://www.econbiz.de/10008872728
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